The Daily will not remove clips of BP testimony despite judge's order.

At BP’s urging, a federal judge ordered The Daily to take down exclusively obtained video clips of deposition testimony by former CEO Tony Hayward from its website — but The Daily is refusing to comply.

Judge Sally Shushan issued the order on Tuesday, saying the release of the video may be in violation of a pretrial order stating that no “part of the video or audio record of a video deposition shall be released or made available to any member of the public unless authorized by the court.”

Hayward gave three days of deposition testimony in a London law office last month as part of a federal lawsuit filed by several states and hundreds of plaintiffs against the oil giant for damages in last year’s Deepwater Horizon oil spill.

The Daily said in a statement yesterday: “We have not removed the clips ... and have no intention of doing so until we’ve had the opportunity to present our case to the court.

“The Deepwater Horizon disaster is one of the worst environmental disasters in United States history and there is tremendous public interest in the complete disclosure of all of the surrounding facts.”

The Daily published the clips on Saturday on its app and website.

The publication contends the judge’s order “is an extraordinary example of prior restraint.” While generally referring to government suppression of speech in advance of publication — a practice prohibited by the First Amendment — “prior restraint” also applies in situations where a court order prevents further publication of material.A source close to the case told The Daily that the judge’s order followed a request from BP’s lawyers that the video be taken down.

“It was counsel for BP that approached the judge and asked for that order,” said the source. “I think there are portions that might be embarrassing to them, including the part where their client is not able to remember the names of the victims.” The reference is to a clip posted by The Daily, in which Hayward is only able to correctly recall the name of one man among the 11 who died when the Deepwater Horizon rig exploded on April 20, 2010.